The 16th Hilbert problem restricted to circular algebraic limit cycles

DOI10.1016/j.jde.2015.12.019zbMath1346.34028OpenAlexW2223478073MaRDI QIDQ2634200

Jaume Llibre, Natalia Sadovskaia, Valentín Ramírez, Rafael O. Ramírez

Publication date: 8 February 2016

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2015.12.019

zbMATH Keywords

Darboux integrabilitypolynomial vector fieldsplanar polynomial differential systeminvariant circles16th Hilbert's problemalgebraic limit cycles

Mathematics Subject Classification ID

Explicit solutions, first integrals of ordinary differential equations (34A05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

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Cites Work

• Unnamed Item
• Inverse problems in ordinary differential equations and applications
• Inverse approach in ordinary differential equations: applications to Lagrangian and Hamiltonian mechanics
• On the 16th Hilbert problem for limit cycles on nonsingular algebraic curves
• The 16th Hilbert problem on algebraic limit cycles
• Lower bounds for the Hilbert number of polynomial systems
• Estimating the number of limit cycles in polynomial systems
• New lower bounds for the Hilbert number of polynomial systems of Liénard type
• On the 16th Hilbert problem for algebraic limit cycles
• Inverse approach to study the planar polynomial vector field with algebraic solutions
• Centennial History of Hilbert's 16th Problem
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• Polynomial vector fields with prescribed algebraic limit cycles

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